Finite Group Databasebeta

← C2×#21446345 #29681991

Subgroups — C2×#21446345 #29681991

Order 15616.

1878 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2C2×#16840331C211yesmaximal, characteristic
3C2×#16839768C211yesmaximal, characteristic, complemented
4C2×#16839766C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6#21446345C218yesmaximal, direct product factor
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×D244C2211yescharacteristic
11#16840528—22no—
12#16840528—22no—
13#16840528—22no—
14#16840528C2214yescomplemented
15C2×#14519785—22no—
16C2×#14519783—22no—
17C22×#11758194C2211yescharacteristic
18C2×M16×D61—22no—
19#16840331—22no—
20#16840331—22no—
21#16840331C414yescomplemented
22#16840331C2214yes—
23C2×#14519774C412yescomplemented
24C2×#14519765C412yescomplemented
25C2×#14519752—22no—
26C2×#14519747—22no—
27C2×#14519736C2211yescharacteristic
28#16839768—22no—
29#16839768C2214yescomplemented
30#16839766—22no—
31#16839766C2214yescomplemented
32C2×#14519699—22no—
33C2×#14519697—22no—
34#16839735—22no—
35#16839735C2214yescomplemented
36C2×#14519691—22no—
37#16839518C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×H(3,ℤ/4)C2214yescomplemented
42C24×D61—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222C2×C412yes—
52C2×#11758222D412yes—
53C2×#11758222D412yes—
54C2×#11758222C2312yes—
55C22×Dic122C2×C411yescharacteristic
56C22×D244—21no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244—21no—
64C22×D244—21no—
65C22×D244—21no—
66C22×D244—21no—
67C22×D244—24no—
68C22×D244C2×C412yes—
69C22×D244C2×C412yes—
70C22×D244C2×C411yescharacteristic
71C22×D244C2312yes—
72C22×C22⋊D61D412yes—
73C22×C4×D61D412yes—
74#14519785—28no—
75#14519785—28no—
76#14519783—28no—
77#14519783—28no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194D412yescomplemented
83C2×#11758194C2312yes—
84C2×#11758189—24no—
85M16×D61—28no—
86M16×D61—28no—
87C22×#92418D412yescomplemented
88C2×C8×D61—24no—
89#14519774—24no—
90#14519774C2×C418yescomplemented
91#14519765—24no—
92#14519765C2×C418yescomplemented
93#14519752—28no—
94#14519752—28no—
95#14519747—28no—
96#14519747—28no—
97#14519736—21no—
98#14519736—21no—
99#14519736—21no—
100#14519736C2312yes—
101C2×C4⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—24no—
104C2×C4×Dic61—21no—
105#14519699—28no—
106#14519697—28no—
107#14519691—28no—
108C23×C4×C61C2311yescharacteristic
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61D412yescomplemented
114C2×M16×C61C2312yes—
115C22×C8×C61D412yescomplemented
116#117×C61—21no—
117#117×C61—21no—
118#117×C61—21no—
119#117×C61—21no—
120#117×C61—21no—
121#117×C61C2×C412yes—
122#117×C61C2312yes—
123#117×C61C2312yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61—21no—
129C2×C42×C61C2×C412yes—
130C24×C61C2×D411yescharacteristic
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—41no—
135C23×D61—41no—
136C23×D61—41no—
137C23×D61—41no—
138C23×D61—84no—
139C23×D61C22⋊C412yes—
140C22×C4×C61—22no—
141C22×C4×C61—41no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61C22⋊C414yes—
161C2×C22⋊D61C2×D414yes—
162C22×Dic61—41no—
163C22×Dic61C22⋊C412yes—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222—22no—
174#11758222—22no—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—22no—
199C2×D244—216no—
200C2×D244—41no—
201C2×D244—41no—
202C2×D244—41no—
203C2×D244—41no—
204C2×D244—41no—
205C2×D244—41no—
206C2×D244—41no—
207C2×D244—41no—
208C2×D244—41no—
209C2×D244—41no—
210C2×D244—41no—
211C2×D244—41no—
212C2×D244—88no—
213C2×D244C22⋊C412yes—
214C2×D244C22×C414yes—
215C2×D244C22×C412yes—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61C22⋊C414yes—
221C2×C4×D61C2×D414yes—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122C22⋊C412yes—
227C2×Dic122C22×C412yes—
228M16×C61—22no—
229M16×C61—22no—
230M16×C61—22no—
231M16×C61—22no—
232C2×C8×C61—22no—
233C2×C8×C61—22no—
234C2×C8×C61C2×D414yescomplemented
235C4⋊C4×C61—22no—
236C4⋊C4×C61—22no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—41no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—41no—
243C42×C61—22no—
244C42×C61—22no—
245C42×C61—41no—
246C42×C61C22×C414yes—
247C22⋊Dic61—22no—
248C22⋊Dic61—41no—
249#11758198—216no—
250C4⋊Dic61—22no—
251C4⋊Dic61—41no—
252C4×Dic61—22no—
253C4×Dic61—41no—
254#11758194—22no—
255#11758194—22no—
256#11758194—22no—
257#11758194—22no—
258C2×#92418—22no—
259C2×#92418—22no—
260C2×#92418C2×D414yescomplemented
261#11758189—216no—
262C8×D61—216no—
263C23×C61—42no—
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61#12111yescharacteristic
267C23×C61#12111yescharacteristic
268C23×C61#12111yescharacteristic
269C23×C61#12111yescharacteristic
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—24no—
274C22×D61—44no—
275C22×D61—48no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61C2×C22⋊C414yes—
289C2×C4×C61—24no—
290C2×C4×C61—44no—
291C2×C4×C61—42no—
292C2×C4×C61—82no—
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61#12011yescharacteristic
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12011yescharacteristic
306C2×C4×C61#12011yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12111yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12311yescharacteristic
312C2×C4×C61#12311yescharacteristic
313C2×C4×C61#12311yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C22⋊D61—24no—
322C22⋊D61—24no—
323C22⋊D61—24no—
324C22⋊D61—24no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—42no—
328C2×Dic61—82no—
329C2×Dic61C2×C22⋊C414yes—
330D244—22no—
331D244—22no—
332D244—24no—
333D244—24no—
334D244—22no—
335D244—22no—
336D244—42no—
337D244—42no—
338D244—42no—
339D244—42no—
340D244—42no—
341D244—42no—
342D244—816no—
343C4×D61—24no—
344C4×D61—24no—
345C4×D61—24no—
346C4×D61—24no—
347Dic122—22no—
348Dic122—22no—
349Dic122—22no—
350Dic122—22no—
351C8×C61—24no—
352#92418—24no—
353C2×#1910—611nomaximal, Sylow
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61#38611yescharacteristic
362C22×C61#38611yescharacteristic
363C22×C61#38611yescharacteristic
364C22×C61#38611yescharacteristic
365C22×C61C22×C22⋊C411yescharacteristic
366C22×C61C2×#12111yescharacteristic
367C22×C61C2×#12111yescharacteristic
368C2×D61—24no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—48no—
372C2×D61—44no—
373C2×D61—82no—
374C2×D61—84no—
375C2×D61—84no—
376C2×D61—84no—
377C2×D61—84no—
378C2×D61—84no—
379C2×D61—84no—
380C4×C61—44no—
381C4×C61—82no—
382C4×C61#38611yescharacteristic
383C4×C61#38611yescharacteristic
384C4×C61#38611yescharacteristic
385C4×C61#38611yescharacteristic
386C4×C61C2×C4×D411yescharacteristic
387C4×C61C2×C4×D411yescharacteristic
388C4×C61C2×#12011yescharacteristic
389C4×C61C2×#12311yescharacteristic
390Dic61—24no—
391Dic61—82no—
392C2×#568—611no—
393C2×#535—611no—
394C2×#418—611no—
395C2×#418—611no—
396C2×#410—611no—
397#1910—618no—
398C2×H(3,ℤ/4)—611no—
399C2×H(3,ℤ/4)D6111yescharacteristic, complemented
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61#191012yescomplemented
407C2×C61C2×#38611yescharacteristic
408D61—44no—
409D61—84no—
410C22×#41—611no—
411C23×D4—611no—
412#568—614no—
413#568—1222no—
414#568—1222no—
415#568—1222no—
416C2×#131—1222no—
417C2×#131—1222no—
418C22×M16—611no—
419C22×M16—1222no—
420C22×M16C2×D6111yescharacteristic
421#535—614no—
422#535—614no—
423#535—1222no—
424#535—1222no—
425C2×#127—612no—
426C2×#124—612no—
427C2×#121—1222no—
428C2×#120—1222no—
429C2×#117—611no—
430C2×#117C2×D6111yescharacteristic
431C2×#117C2×D6111yescharacteristic
432#418—614no—
433#418—614no—
434#418—1222no—
435#418—1222no—
436C2×#102—1222no—
437C2×#102—1222no—
438#410—614no—
439#410—1222no—
440C2×#99—1222no—
441H(3,ℤ/4)—614no—
442H(3,ℤ/4)C2×D6114yescomplemented
443C61C2×#191011yescharacteristic, complemented, Sylow
444C25—1221no—
445C2×#41—612no—
446C2×#41—612no—
447C2×#41—612no—
448C2×#41—612no—
449C2×#41—1221no—
450C2×#41—1221no—
451C2×#41—1221no—
452C2×#41—1221no—
453C2×#41—1221no—
454C2×#41—1221no—
455C2×#41—1221no—
456C2×#41—1221no—
457C22×Q8—611no—
458C22×D4—612no—
459C22×D4—611no—
460C22×D4—612no—
461C22×D4—612no—
462C22×D4—612no—
463C22×D4—1224no—
464C22×D4—1221no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1221no—
475C23×C4—612no—
476C23×C4C22×D6111yescharacteristic
477#131—1228no—
478#131—1228no—
479#131—1228no—
480#131—1228no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—612no—
486C2×M16—612no—
487C2×M16—1224no—
488C2×M16—1228no—
489C2×M16—1228no—
490C2×M16—1221no—
491C2×M16—1221no—
492C2×M16—1221no—
493C2×M16—1221no—
494C2×M16D24412yescomplemented
495C2×M16C22×D6112yes—
496C22×C8—612no—
497C22×C8—1224no—
498C22×C8D24412yescomplemented
499#127—618no—
500#127—1224no—
501#124—618no—
502#124—1224no—
503#121—1228no—
504#121—1228no—
505#120—1228no—
506#120—1228no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—612no—
513#117—1221no—
514#117—1221no—
515#117—1221no—
516#117C4×D6112yes—
517#117C22×D6112yes—
518#117C22×D6112yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—1221no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1224no—
525C2×C22⋊C4—1221no—
526C2×C42—21no—
527C2×C42—1221no—
528C2×C42C4×D6112yes—
529#102—1228no—
530#102—1228no—
531#99—1228no—
532C24—612no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—4884no—
537C24—2441no—
538C24—2441no—
539C24—2441no—
540C24—2441no—
541C24D4×D6111yescharacteristic
542#41—1222no—
543#41—1222no—
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—1222no—
551#41—1222no—
552#41—1222no—
553#41—1222no—
554#41—1222no—
555#41—1222no—
556#41—1222no—
557#41—1222no—
558C2×Q8—612no—
559C2×Q8—612no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×D4—614no—
565C2×D4—614no—
566C2×D4—612no—
567C2×D4—614no—
568C2×D4—612no—
569C2×D4—12216no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—4888no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C2×D4—2441no—
601C2×D4—2441no—
602C2×D4—2441no—
603C2×D4—2441no—
604C2×D4—2441no—
605C2×D4—2441no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—612no—
609C22×C4—614no—
610C22×C4—614no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2441no—
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6111yescharacteristic
618C22×C4C2×D24411yescharacteristic
619C22×C4C2×D24411yescharacteristic
620C22×C4#1175822211yescharacteristic
621C22×C4#1175822211yescharacteristic
622C22×C4D4×D6111yescharacteristic
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4D4×D6111yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C22×C4#1175822611yescharacteristic
628C22×C4#1175822611yescharacteristic
629C22×C4C23×D6111yescharacteristic
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—12216no—
635M16—1222no—
636M16—1222no—
637M16—1222no—
638M16—1222no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—614no—
642C2×C8—12216no—
643C2×C8—1222no—
644C2×C8—1222no—
645C2×C8C2×D24414yescomplemented
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—1222no—
651C4⋊C4—2441no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—12216no—
657C22⋊C4—1222no—
658C22⋊C4—2441no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—1222no—
663C42—2441no—
664C42C2×C4×D6114yes—
665C23—42no—
666C23—614no—
667C23—1222no—
668C23—1222no—
669C23—1224no—
670C23—4884no—
671C23—4884no—
672C23—4884no—
673C23—4884no—
674C23—4884no—
675C23—4884no—
676C23—2448no—
677C23—2444no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23C22⋊C4×D6111yescharacteristic
685C23C22⋊C4×D6111yescharacteristic
686C23#1451975011yescharacteristic
687C23#1451975011yescharacteristic
688C23#1451975211yescharacteristic
689C23#1451975211yescharacteristic
690C23C2×D4×D6111yescharacteristic
691Q8—1222no—
692Q8—1222no—
693Q8—1222no—
694Q8—1222no—
695D4—1224no—
696D4—1224no—
697D4—1224no—
698D4—1224no—
699D4—1222no—
700D4—1224no—
701D4—1222no—
702D4—1224no—
703D4—1222no—
704D4—1222no—
705D4—48816no—
706D4—2442no—
707D4—2442no—
708D4—2442no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—82no—
716C2×C4—614no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1224no—
720C2×C4—1224no—
721C2×C4—1224no—
722C2×C4—1224no—
723C2×C4—4882no—
724C2×C4—2442no—
725C2×C4C22⋊C4×D6111yescharacteristic
726C2×C4C22⋊C4×D6111yescharacteristic
727C2×C4#1451973911yescharacteristic
728C2×C4#1451973911yescharacteristic
729C2×C4#1451973911yescharacteristic
730C2×C4#1451973911yescharacteristic
731C2×C4C4×D24411yescharacteristic
732C2×C4C4×D24411yescharacteristic
733C2×C4C4×D24411yescharacteristic
734C2×C4C4×D24411yescharacteristic
735C2×C4#1451974711yescharacteristic
736C2×C4#1451974711yescharacteristic
737C2×C4#1451974711yescharacteristic
738C2×C4#1451974711yescharacteristic
739C2×C4#1451975011yescharacteristic
740C2×C4#1451975011yescharacteristic
741C2×C4#1451975211yescharacteristic
742C2×C4#1451975211yescharacteristic
743C2×C4#1451976211yescharacteristic
744C2×C4#1451976211yescharacteristic
745C2×C4#1451976211yescharacteristic
746C2×C4#1451976211yescharacteristic
747C2×C4C22×C4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C2×D4×D6111yescharacteristic
750C2×C4C22×D24411yescharacteristic
751C2×C4C2×#1175822211yescharacteristic
752C2×C4C2×#1175822611yescharacteristic
753C8—24no—
754C8—1224no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—1224no—
763C22—4884no—
764C22—4884no—
765C22—4884no—
766C22—4884no—
767C22—4884no—
768C22—4882no—
769C22—4884no—
770C22—2448no—
771C22—2444no—
772C22—2444no—
773C22—2444no—
774C22#1683964011yescharacteristic
775C22#1683964011yescharacteristic
776C22#1683964011yescharacteristic
777C22#1683964011yescharacteristic
778C22C2×C22⋊C4×D6111yescharacteristic
779C22C2×#1451975011yescharacteristic
780C22C2×#1451975211yescharacteristic
781C4—44no—
782C4—82no—
783C4—1224no—
784C4—4882no—
785C4#1683964011yescharacteristic
786C4#1683964011yescharacteristic
787C4#1683964011yescharacteristic
788C4#1683964011yescharacteristic
789C4C2×#1451973911yescharacteristic
790C4C2×C4×D24411yescharacteristic
791C4C2×#1451974711yescharacteristic
792C4C2×#1451976211yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—4884no—
800C2—2444no—
801C2#2144634512yesdirect product factor
802C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC22×C61#386
prime radicalC2×#16840331C2
cosocleC22×C4×C61C24
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61C2×#1910
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839768C2semidirect
4. C2×#16839766C2semidirect
5. C2×#16839735C2semidirect
6. #21446345C2direct (N × H)
7. C2×#16839518C2semidirect
8. C2×C61×H(3,ℤ/4)C2semidirect
14. #16840528C22semidirect
21. #16840331C4semidirect
23. C2×#14519774C4semidirect
24. C2×#14519765C4semidirect
29. #16839768C22semidirect
31. #16839766C22semidirect
35. #16839735C22semidirect
37. #16839518C22semidirect
41. C61×H(3,ℤ/4)C22semidirect
82. C2×#11758194D4semidirect
87. C22×#92418D4semidirect
90. #14519774C2×C4semidirect
92. #14519765C2×C4semidirect
113. C2×M16×C61D4semidirect
115. C22×C8×C61D4semidirect
234. C2×C8×C61C2×D4semidirect
260. C2×#92418C2×D4semidirect
399. C2×H(3,ℤ/4)D61semidirect
406. C2×C61#1910semidirect
442. H(3,ℤ/4)C2×D61semidirect
443. C61C2×#1910semidirect
494. C2×M16D244semidirect
498. C22×C8D244semidirect
645. C2×C8C2×D244semidirect
801. C2#21446345direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168405282
C2×#168403312
C2×#168397682
C2×#168397662
C2×#168397352
#214463452
C2×#168395182
C2×C61×H(3,ℤ/4)2
C2×#191061